Question

Use the diagram and problem below to find the missing anglemeasure.

Answer 1

Given:

BAC = 33 degrees

BDC = 35 degrees

Solution:

From the properties of an isosceles triangle:

The base angles of an isosceles triangle are equal. Hence from triangle BDC, we have:

`\angle\text{BDC = }\angle\text{BCD = 35}^0`

We can obtain angle DBC using the theorem that the sum of angles in a triangle is 180 degrees:

`\begin{gathered} \angle DBC=180^0-35^0-35^0 \\ =110^0 \end{gathered}`

To find angle ABD, we use the theorem of congruency. i.e

`\Delta\text{ ABD }\cong\text{ }\Delta\text{ ABC}`

Hence,

`\angle\text{ ABD = }\angle\text{ ABC}`

Since the angles ABD, ABC and DBC lie at a point, we have:

`\begin{gathered} Let\text{ }\angle\text{ ABD = x} \\ x+x+110^0=360^0 \\ 2x=250^0 \\ x=125^0 \end{gathered}`

Answer : angle ABD = 125 degrees